It can help, but other degrees also have content writing value. For instance, the ability to synthesize and relate complex information is key to content writing, but can also be acquired from studies in education or philosophy. Companies that offer content writing positions tend to find it easier to train someone in a complex topic than to train someone to write, however. For example, as a healthcare professional with mediocre writing skills, you're less likely to be hired as a healthcare content writer than a strong writer with no healthcare background (but who can be trained in healthcare topics).
Predictably, blog posts are typically written by the bloggers. However, if your team is large enough to have someone dedicated to creating gated assets and premium content -- things like ebooks and tools -- they should also write blog posts to help promote those assets. SEO specialists will also work closely with bloggers, as blog posts are often a company's best opportunity to improve organic search rankings. As such, bloggers should be writing posts that help improve the site's SEO, and drive organic traffic and leads. Their editorial should be informed by keyword research, and optimized for SEO.